A rectangle has a perimeter of 24 ft. Following a dilation, the new perimeter of the

Mathematics

1 answer:

nasty-shy [4]2 years ago

4 0

Answer:

it has increased by 1/2 so the scale factor would either be 3/2 or 1.5 or something

Step-by-step explanation:

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Prove that the difference between a two-digit number and the product of its digits will always be a 2 digit number.

slamgirl [31]

Step-by-step explanation:

Let the two-digit number is $xy$

<u>This can be written as:</u>

10x + y, where 1 ≤ x ≤ 9 and 0 ≤ y ≤ 9

<u>The difference between the number and product of its digits is:</u>

d = 10x + y - xy

<u>Rewrite this as below:</u>

d = 10x - xy + y - 10 + 10 =

x(10 - y) - (10 - y) + 10 =

(x - 1)(10 - y) + 10

0 ≤ x - 1 ≤ 8 according to the condition given above
1 ≤ 10 - y ≤ 10 again according to the condition given above

<u>The value of d is then:</u>

0 + 10 ≤ d ≤ 8*10 + 10
10 ≤ d ≤ 90

<h3>Proved</h3>

7 0

2 years ago

Read 2 more answers

A-b

Lynna [10]

Answer:

$\boxed{\sf d. \ \frac{a}{b} = \frac{10}{7}}$

Step-by-step explanation:

$\sf \implies \dfrac{a - b}{b} = \dfrac{3}{7} \\ \\ \sf \implies \frac{a}{b} - \frac{b}{b} = \frac{3}{7} \\ \\ \sf \implies \frac{a}{b} - 1 = \frac{3}{7} \\ \\ \sf \implies \frac{a}{b} - 1 + 1 = \frac{3}{7} + 1 \\ \\ \sf \implies \frac{a}{b} = \frac{3}{7} + 1 \\ \\ \sf \implies \frac{a}{b} = \frac{3}{7} + \frac{7}{7} \\ \\ \sf \implies \frac{a}{b} = \frac{3 + 7}{7} \\ \\ \sf \implies \frac{a}{b} = \frac{10}{7}$